In this paper, the performance of a compact Three-Fluid Combined Membrane Contactor (3F-CMC) is investigated using Computational Fluid Dynamics (CFD), supported and validated with a good agreement by an experimental campaign made on a fully working prototype. This internally-cooled membrane contactor is the core component of a hybrid air conditioning system for electric vehicles (EVs) developed in a successful H2020 project called XERIC. In the adopted numerical approach, the conjugate heat and mass transfer inside the 3F-CMC is described by non-isothermal incompressible flows and vapor transport through a PTFE hydrophobic membrane. The sensitivity of the 3F-CMC performance to air/desiccant flow rates, temperature, humidity, and desiccant concentration is analyzed numerically through the validated CFD codes. According to this study, the moisture removal increases by the inlet humidity ratio, nearly linearly. Under the considered conditions (where the inlet air temperature is 26.2 °C), when the inlet relative humidity (RH) is 75% the moisture removal is about 450% higher than the case RH = 37%, while the absorption effectiveness declines about 45%. Furthermore, this study shows that the amount of absorbed vapor flux rises by increasing the airflow rate; on the other hand, the higher the airflow rate, the lower is the overall absorption efficiency of the 3F-CMC. This investigation gives important suggestions on how to properly operate a 3F-CMC in order to achieve the requested performance, especially in hot and humid climates.